Gottfried Wilhelm Leibniz (also spelled Leibnitz; born July 1, 1646 [Old Style June 21] – died November 14, 1716) was a German expert in many areas, including mathematics, philosophy, science, and diplomacy. He is known, along with Isaac Newton, for creating calculus and for work in other areas of mathematics, such as binary arithmetic and statistics. Leibniz was called the "last universal genius" because he had knowledge in many fields, a rarity after his time due to the Industrial Revolution and the rise of specialized jobs. He is important in the history of philosophy and mathematics. He wrote about philosophy, theology, ethics, politics, law, history, languages, games, music, and other subjects. He also contributed to physics and technology and introduced ideas that later appeared in probability theory, biology, medicine, geology, psychology, linguistics, and computer science.

Leibniz helped develop a cataloging system for the Herzog August Library in Wolfenbüttel, Germany, which became a model for many large European libraries. His work on many subjects was spread across journals, letters, and unpublished writings. He wrote in several languages, mainly Latin, French, and German.

As a philosopher, he was a major figure in 17th-century rationalism and idealism. As a mathematician, he created differential and integral calculus independently of Newton’s similar work. His notation is widely used as the standard way to express calculus. He also created the modern binary number system, which is the basis of modern communication and computing. Though Thomas Harriot, an English astronomer, developed the same system earlier, Leibniz is credited with its modern form. He introduced the idea of combinatorial topology in 1679 and helped start the field of fractional calculus.

In the 20th century, Leibniz’s ideas about the law of continuity and the transcendental law of homogeneity were given a clear mathematical form through non-standard analysis. He was also an early innovator in mechanical calculators. While improving Pascal’s calculator to add automatic multiplication and division, he described the first pinwheel calculator in 1685 and invented the Leibniz wheel, which was used in the arithmometer, the first widely produced mechanical calculator.

In philosophy and theology, Leibniz is known for his belief that our world is the best possible world God could have created, a view criticized by others like Voltaire in his book Candide. He was one of three major early modern rationalists, along with René Descartes and Baruch Spinoza. His philosophy included ideas from the scholastic tradition, such as the belief that knowledge can be gained by reasoning from basic principles. His work influenced modern logic and continues to affect contemporary analytic philosophy, including the use of the term "possible world" to explain ideas about possibility and necessity.

Biography

Gottfried Leibniz was born on July 1, 1646, in Leipzig, in the Electorate of Saxony, which is now part of the German state of Saxony. His parents were Friedrich Leibniz and Catharina Schmuck. He was baptized two days later at St. Nicholas Church in Leipzig. His godfather was Martin Geier, a Lutheran theologian. His father died when Leibniz was six years old, and his mother raised him.

Leibniz’s father had been a professor of Moral Philosophy at the University of Leipzig and also served as a dean of philosophy. Leibniz inherited his father’s personal library and was allowed to use it freely from the age of seven, shortly after his father’s death. While his schoolwork focused on a small group of required texts, the library let him study many advanced philosophical and theological works that he would not have read until college. His father’s library, mostly in Latin, helped him become skilled in the Latin language by age 12. At 13, he wrote 300 lines of Latin verse in one morning for a school event.

In April 1661, at age 14, Leibniz enrolled at the University of Leipzig, where his father had once studied. He was guided by Jakob Thomasius, who had been a student of Leibniz’s father. Leibniz earned his bachelor’s degree in Philosophy in December 1662. In June 1663, he defended a paper titled Metaphysical Disputation on the Principle of Individuation, which discussed the principle of individuation and introduced an early version of monadic substance theory. He earned his master’s degree in Philosophy in February 1664. In December 1664, he published and defended a paper titled An Essay of Collected Philosophical Problems of Right, arguing for the connection between philosophy and law. After one year of legal studies, he received his bachelor’s degree in Law in September 1665. His dissertation was titled On Conditions.

In early 1666, at age 19, Leibniz wrote his first book, On the Combinatorial Art, which was also his habilitation thesis in Philosophy. He defended it in March 1666. The book was inspired by Ramon Llull’s Ars Magna and included a proof of God’s existence based on the argument from motion.

Leibniz next aimed to earn his license and Doctorate in Law, which usually required three years of study. In 1666, the University of Leipzig rejected his doctoral application, likely because he was too young. He left Leipzig and enrolled at the University of Altdorf. He quickly submitted a thesis titled Inaugural Disputation on Ambiguous Legal Cases. He earned his license to practice law and his Doctorate in Law in November 1666. He then declined an academic position at Altdorf, saying his thoughts were focused on other work.

As an adult, Leibniz often introduced himself as “Gottfried von Leibniz.” Some published editions of his work listed his name as “Freiherr G. W. von Leibniz.” However, no documents from his time show he was officially granted nobility.

Leibniz’s first job was as a paid secretary for an alchemical society in Nuremberg. He knew little about alchemy but presented himself as knowledgeable. He soon met Johann Christian von Boyneburg, a former chief minister of the Elector of Mainz. Von Boyneburg hired Leibniz as an assistant and later introduced him to the Elector. Leibniz wrote an essay on law for the Elector, hoping to get a job. The Elector asked him to help rewrite the legal code for the Electorate. In 1669, Leibniz became an assessor in the Court of Appeal. After von Boyneburg’s death in 1672, Leibniz worked for von Boyneburg’s widow until she dismissed him in 1674.

Von Boyneburg helped raise Leibniz’s reputation, and his writings began to gain attention. After working for the Elector, Leibniz took on a diplomatic role. He published an essay under a fake Polish nobleman’s name, arguing (unsuccessfully) for a German candidate to become king of Poland. During Leibniz’s adult life, Louis XIV of France was a major European power. The Thirty Years’ War had left German-speaking Europe weakened and economically poor. Leibniz proposed a plan to distract France by offering Egypt as a stepping stone for France to attack the Dutch East Indies. In return, France would leave Germany and the Netherlands alone. The Elector supported the idea cautiously. In 1672, France invited Leibniz to Paris to discuss the plan, but the plan became irrelevant after the Franco-Dutch War began. Napoleon’s failed invasion of Egypt in 1798 later resembled Leibniz’s plan, though it came too late.

Leibniz went to Paris in 1672. He met Christiaan Huygens, a Dutch physicist and mathematician, and realized he needed to improve his math and physics knowledge. With Huygens’s help, he studied hard and made major contributions to both fields, including developing his own version of calculus. He also met French philosophers Nicolas Malebranche and Antoine Arnauld and studied the works of Descartes and Pascal. He became friends with Ehrenfried Walther von Tschirnhaus, a German mathematician, and they stayed in contact for life.

When France did not follow through on Leibniz’s plan, the Elector sent his nephew to London with Leibniz to discuss related matters. In London, Leibniz met Henry Oldenburg and John Collins and demonstrated a calculating machine he had designed since 1670. The machine could add, subtract, multiply, and divide. The Royal Society made him an external member.

The mission ended quickly when news of the Elector’s death in February 1673 reached them. Leibniz returned to Paris instead of going back to Mainz. The sudden deaths of his two patrons left him without support, forcing him to find a new career path.

A 1669 invitation from Duke John Frederick of Brunswick to visit Hanover proved important. Leibniz had declined it but had started corresponding with the duke in 1671. In 1673, the duke offered Leibniz a position as a counsellor. He reluctantly accepted two years later, after realizing no jobs were available in Paris or with the Habsburgs.

Philosophy

Leibniz’s philosophical ideas seem scattered because most of his writings are short pieces, such as journal articles, letters, and manuscripts published after his death. He wrote two longer philosophical works, but only one, the Théodicée (a book published in 1710), was released during his lifetime.

Leibniz considered his Discourse on Metaphysics, written in 1686, as the start of his philosophical career. This work was a response to a debate between Nicolas Malebranche and Antoine Arnauld. Leibniz exchanged many letters with Arnauld about this topic, but these writings and the Discourse were not published until the 19th century. In 1695, Leibniz introduced his ideas to European philosophy through a journal article titled New System of the Nature and Communication of Substances. Between 1695 and 1705, he wrote New Essays on Human Understanding, a detailed response to John Locke’s An Essay Concerning Human Understanding (1690). However, after learning of Locke’s death in 1704, Leibniz lost interest in publishing the New Essays, which were not released until 1765. The Monadologie, written in 1714, was published after Leibniz’s death and contains 90 short statements.

Leibniz also wrote a short paper titled Primae veritates (meaning "first truths"), which was first published in 1903 by Louis Couturat. This paper summarized Leibniz’s views on metaphysics. It was undated, but scholars later discovered it was written in Vienna in 1689. This finding came in 1999, when a major project to collect and study Leibniz’s writings published his works from 1677 to 1690. Couturat’s interpretation of Primae veritates influenced many 20th-century philosophers, especially analytic philosophers. However, after studying Leibniz’s writings up to 1688 and considering new discoveries, Mercer (2001) disagreed with Couturat’s interpretation.

In 1676, Leibniz met Baruch Spinoza, read some of Spinoza’s unpublished works, and was influenced by some of his ideas. Although Leibniz admired Spinoza’s intellect, he disagreed with some of Spinoza’s conclusions, especially those that conflicted with Christian beliefs.

Unlike Descartes and Spinoza, Leibniz had a university education in philosophy. He studied under Jakob Thomasius, a professor in Leipzig, who also supervised his Bachelor of Arts thesis in philosophy. Leibniz also read Francisco Suárez, a respected Spanish Jesuit. He was interested in the new scientific methods of Descartes, Huygens, Newton, and Boyle, but his education in traditional philosophy shaped how he understood their work.

Leibniz used seven key philosophical principles in his thinking:

• Identity / Contradiction: If a statement is true, its opposite is false, and vice versa.
• Identity of Indiscernibles: If two things share all the same properties, they are actually the same thing. This idea is often used in modern logic and has been debated in science.
• Sufficient Reason: Everything has a reason for existing or happening.
• Pre-established Harmony: Each substance in the universe acts in harmony with others without directly affecting them. For example, a glass shatters because it "knows" it has hit the ground, not because the ground forces it to break.
• Law of Continuity: Nature does not make sudden jumps.
• Optimism: God always chooses the best possible outcome.
• Plenitude: The best possible world includes all genuine possibilities.

Leibniz sometimes explained these principles in detail, but often treated them as basic truths.

Leibniz’s most famous contribution to metaphysics is his theory of monads, as described in the Monadologie. He argued that the universe is made of an infinite number of simple substances called monads. Unlike atoms, monads have no parts and are not affected by space or time. They exist only through their qualities, which change over time. Each monad is unique and follows its own set of "instructions," allowing it to act independently. Monads are like mirrors of the universe, reflecting all other monads. They are not limited in size; for example, humans are considered monads, which raises questions about free will.

Leibniz’s theory of monads addressed problems in earlier philosophies:

• It avoided the difficulty of explaining how mind and matter interact, as in Descartes’ system.
• It solved the issue of how individual beings are distinct, which was a challenge in Spinoza’s system.

In the Théodicée, Leibniz argued that the world, though imperfect, is the best possible one. He used a geometry book as an example, explaining that the book’s content must have a reason for existing. He concluded that the ultimate reason for everything is God, whom he called the "monas monadum" (the "monad of monads").

Monads are defined by their basic simplicity. Unlike atoms, they have no physical or spatial qualities. They do not depend on each other, but they act in harmony due to a prearranged plan. This harmony allows each monad to "know" what to do at any moment, as if following a set of instructions. Because of this, each monad reflects the entire universe, like a tiny mirror. Monads can be large, such as humans, which raises questions about free will.

The Théodicée attempts to explain why the world has imperfections by arguing that it is the best possible world among all possible ones.

Mathematics

Leibniz was the first person to use the mathematical idea of a function clearly in 1692 and 1694. He used it to describe several geometric ideas related to curves, such as abscissa, ordinate, tangent, chord, and perpendicular. By the 18th century, the term "function" no longer had strong connections to geometry. Leibniz also helped develop actuarial science, calculating the cost of life annuities and ways to pay off a state's debt.

Leibniz's work on formal logic, which is important to mathematics, is discussed in a previous section. A detailed overview of his writings on calculus can be found in Bos's book from 1974.

Leibniz created one of the first mechanical calculators. He once said, "It is not fitting for great people to waste hours like workers in the hard task of calculation, which could be done by others if machines were used."

Leibniz organized the numbers in a system of linear equations into a grid, now called a matrix, to find solutions. This method later became known as Gaussian elimination. He also developed the theory of determinants, though a Japanese mathematician named Seki Takakazu discovered determinants independently. Leibniz used a method called cofactor expansion to calculate determinants, which is now called the Leibniz formula. This method becomes impractical for large matrices because it requires calculating many products. He also solved systems of equations using determinants, a method now called Cramer's rule. Leibniz discovered this method in 1684, while Cramer published his findings in 1750. Although Gaussian elimination requires fewer steps, many math textbooks still teach cofactor expansion before other methods.

The Leibniz formula for π shows that π can be written as an alternating series of fractions. Leibniz wrote that circles can be described by this series, which adds and subtracts fractions. However, this formula needs many terms to be accurate. For example, it would take 10 million terms to calculate π/4 to eight decimal places. Leibniz also tried to define a straight line while working on the parallel postulate. Most mathematicians defined a straight line as the shortest path between two points, but Leibniz believed this was a property, not the definition.

Leibniz is credited, along with Isaac Newton, with inventing calculus. According to his notes, he made a major breakthrough on November 11, 1675, when he used integral calculus to find the area under a function's graph. He introduced symbols still used today, such as the integral sign ∫ (from the Latin word summa, meaning "sum") and the notation dy/dx (from the Latin word differentia, meaning "difference"). He did not publish his work on calculus until 1684. Leibniz showed the relationship between integration and differentiation, later called the fundamental theorem of calculus, in a 1693 paper. James Gregory, Isaac Barrow, and Isaac Newton also contributed to this idea. The product rule in calculus is still called "Leibniz's law." The rule for differentiating under an integral sign is called the Leibniz integral rule.

Leibniz used infinitesimals in his calculus work, treating them in ways that seemed to have unusual properties. George Berkeley criticized these ideas in writings like The Analyst. A recent study suggests that Leibniz's approach was logically sound and better than Berkeley's criticisms.

Leibniz introduced fractional calculus in a letter to Guillaume de l'Hôpital in 1695. He also discussed derivatives of "general order" with Johann Bernoulli. In a letter to John Wallis in 1697, Wallis's infinite product for π/2 was discussed. Leibniz suggested using differential calculus to find this result. He used the notation d^(1/2)y to represent a derivative of order 1/2.

From 1711 until his death, Leibniz argued with John Keill, Newton, and others about whether he invented calculus independently of Newton.

Infinitesimals were not widely accepted by followers of Karl Weierstrass, but they remained useful in science, engineering, and even in advanced mathematics through the concept of the differential. In 1960, Abraham Robinson created a rigorous system for infinitesimals using hyperreal numbers. This system, called non-standard analysis, supported Leibniz's methods. Robinson's transfer principle and the standard part function relate to Leibniz's ideas about continuity and homogeneity.

Leibniz was the first to use the term "analysis situs," later known as topology. Some scholars, like Mates, argue that Leibniz's work influenced later developments in topology. Others, like Hideaki Hirano, note that Leibniz's ideas about self-similarity and continuity inspired fractal geometry. Leibniz described a straight line as a curve where every part resembles the whole, an idea that foreshadowed topology. He also imagined a process of repeatedly placing smaller circles inside larger ones, an early concept of self-similarity. In his work Characteristica Geometrica, Leibniz aimed to describe geometric properties with symbols and operations, laying the foundation for combinatorial topology.

Science and engineering

Leibniz's writings are still studied today, not only because they include ideas that were ahead of their time but also because they help improve our current understanding of science. Many of his physics writings can be found in Gerhardt's Mathematical Writings.

Leibniz made important contributions to the study of motion and forces, often disagreeing with scientists like Descartes and Newton. He created a new theory of motion based on energy, which suggested that space is not fixed but changes depending on how things move. Newton, however, believed space was always the same. A key example of Leibniz's work in physics is his book Specimen Dynamicum from 1695.

Before scientists discovered tiny particles and the rules of quantum mechanics, many of Leibniz's ideas about the nature of the universe seemed strange. For example, he argued that space, time, and movement are not fixed, which was similar to ideas later proposed by Albert Einstein. He once said, "I believe space is relative, just like time, and it is the order in which things exist together."

Leibniz believed that space and time are not separate things but are instead ways to describe how objects relate to each other. This idea contrasts with Newton's view that space and time exist on their own. Later discoveries in physics, like Einstein's theory of relativity, have made Leibniz's ideas seem more correct.

One of Leibniz's goals was to explain Newton's ideas using a theory about swirling motion called a vortex. However, his work went beyond this, as he tried to explain how matter holds together, a big question in science.

Leibniz's ideas have influenced modern science in many ways. For example, his concept of "vis viva," or "living force," is related to energy, and he believed energy is always conserved in certain systems. His ideas sometimes caused arguments between scientists in different countries, but both energy and momentum are actually conserved in physics. In Einstein's theory of relativity, energy and momentum are connected in a complex way.

Leibniz also made early predictions about the Earth's structure, suggesting it has a molten core, which matches modern geology. In biology, he studied how life forms develop and thought that living things result from many possible structures. He also studied fossils and believed that species can change over time, an idea that later scientists supported. One of his books, Protogaea, was published long after his death.

In medicine, Leibniz encouraged doctors to use careful observations and experiments instead of relying on ideas that were not proven.

Psychology was an important interest for Leibniz. He wrote about topics like memory, learning, and how the mind works, which are now part of psychology. He used simple examples, like the behavior of a dog or the sound of the sea, to explain his ideas. He also proposed that the mind and body work together in harmony, even though they are separate. He believed that the mind can influence the body and vice versa, but they do not directly affect each other.

Leibniz's ideas influenced later scientists, including Wilhelm Wundt, who helped create psychology as

Law and morality

English-speaking scholars did not pay much attention to Leibniz's writings on law, ethics, and politics for a long time. However, this has changed.

Leibniz was not a supporter of absolute monarchy, like Hobbes, nor did he support any form of tyranny. He also did not share the political and constitutional views of John Locke, whose ideas were used to support liberalism in 18th-century America and other places. A letter from 1695 to Baron J. C. Boyneburg's son, Philipp, shows Leibniz's political beliefs clearly.

In 1677, Leibniz proposed a European confederation led by a council or senate, where members would represent entire nations and vote freely. This idea is sometimes seen as an early version of the European Union. He also believed Europe would adopt a single religion. He repeated these ideas in 1715.

At the same time, Leibniz worked to create a universal system of justice that required knowledge from many fields. He combined linguistics (especially studies of Chinese), moral and legal philosophy, management, economics, and politics to support his ideas.

Leibniz studied law but was influenced by Erhard Weigel, a supporter of Cartesian ideas. Weigel encouraged using mathematical methods to solve legal problems, which is visible in Leibniz's work, such as Specimen Quaestionum Philosophicarum ex Jure collectarum ("An Essay of Collected Philosophical Problems of Right"). For example, Disputatio Inauguralis de Casibus Perplexis in Jure ("Inaugural Disputation on Ambiguous Legal Cases") used early combinatorics to resolve legal disputes, and De Arte Combinatoria ("On the Art of Combination") included legal examples.

The use of combinatorial methods in law and ethics may have been inspired by Ramón Llull, who tried to solve religious disputes using a universal system of reasoning.

In the late 1660s, Prince-Bishop Johann Philipp von Schönborn of Mainz announced a review of the legal system and offered a position to support his law commissioner. Leibniz left Franconia and traveled to Mainz before securing the job. In Frankfurt am Main, he wrote The New Method of Teaching and Learning the Law, which proposed reforms to legal education. The text combined ideas from Thomism, Hobbesianism, Cartesianism, and traditional jurisprudence. Leibniz argued that legal education should help students discover their own public reason, not simply memorize rules. This idea impressed von Schönborn, who hired him.

While working in Mainz from 1667 to 1672, Leibniz sought a universal rational basis for law, aiming to create a "science of right." Starting with Hobbes' ideas about power, he turned to logical and combinatorial methods to define justice. In Elementa Juris Naturalis, he introduced ideas about possibility and necessity, which may be the earliest version of his "possible worlds" theory within a legal framework. Though Elementa was never published, Leibniz continued to refine and share its ideas until his death.

Leibniz also worked to unite the Roman Catholic and Lutheran churches, following the example of his early supporters, Baron von Boyneburg and Duke John Frederick, who had converted to Catholicism as adults. These efforts included correspondence with French bishop Jacques-Bénigne Bossuet and participation in theological debates. Leibniz believed that applying reason thoroughly could resolve the divisions caused by the Reformation.

Philology

Leibniz, a language expert, was very interested in studying languages. He was excited to learn about vocabulary and grammar whenever he could. In 1710, he used ideas about slow changes over time and the idea that the same processes happen now as in the past to study languages. He disagreed with the belief that Hebrew was the first language of humans. At the same time, he believed all languages had a common origin. He also disagreed with the idea that an early form of Swedish was the ancestor of Germanic languages. He was curious about where Slavic languages came from and was fascinated by classical Chinese. He was skilled in the Sanskrit language.

He published the first modern edition of the Latin chronicle called Chronicon Holtzatiae, which recorded events in the County of Holstein.

Sinophilia

Leibniz was one of the first important European thinkers to study Chinese culture closely. He learned about China by reading works written by European Christian missionaries who lived in China and by communicating with them. He read a book called Confucius Sinarum Philosophus in the year it was first published. He believed that Europeans could learn valuable lessons from the ethical teachings of Confucianism. He considered the possibility that Chinese characters might be an accidental example of his idea for a universal system of symbols. He observed that the hexagrams in the I Ching match the binary numbers from 000000 to 111111 and saw this as proof of significant Chinese achievements in the type of mathematical philosophy he admired. Leibniz shared his ideas about the binary system representing Christianity with the Emperor of China, hoping it would lead to the Emperor’s conversion. He was one of the Western philosophers of his time who tried to connect Confucian ideas with European beliefs.

Leibniz’s interest in Chinese philosophy came from his belief that it shared similarities with his own ideas. Historian E.R. Hughes suggests that Leibniz’s concepts of "simple substance" and "pre-established harmony" were directly influenced by Confucianism, as these ideas were developed during the time he was reading Confucius Sinarum Philosophus.

Polymath

During his long trip to European records to study the history of the Brunswick family, which he never finished, Leibniz visited Vienna between May 1688 and February 1689. There, he helped with official matters for the Brunswicks. He toured mines, spoke with engineers, and tried to make deals to sell lead from the ducal mines in the Harz mountains. His idea to light Vienna’s streets with lamps using oil from rapeseed plants was put into action. During an official meeting with the Austrian Emperor and in later written reports, he suggested changing how Austria’s economy works, improving money systems in much of central Europe, making an agreement between the Habsburgs and the Vatican, and building a large library for research, an official archive, and a fund for public safety. He also wrote and published an important article about how machines work.

Posthumous reputation

After Leibniz died, his reputation was not as strong as it had been. People mainly remembered him for one book, Théodicée, which Voltaire mocked in his famous book Candide. In Candide, the character says "non liquet," a Latin phrase meaning "it is not clear." This term was used in ancient Rome to describe a legal decision of "not proven." Voltaire’s portrayal of Leibniz’s ideas became so widely known that many people believed it was accurate. Because of this, Voltaire and his book Candide contributed to the slow recognition of Leibniz’s true ideas. Leibniz had a devoted follower named Christian Wolff, whose strict and overly simple ideas hurt Leibniz’s reputation. Leibniz also influenced David Hume, who read Théodicée and used some of its ideas. At the time, philosophical trends were moving away from the detailed systems and rational thinking that Leibniz supported. His work on law, diplomacy, and history was seen as unimportant. The large number of letters he wrote was not widely recognized.

Leibniz’s reputation began to improve in 1765 with the publication of Nouveaux Essais. In 1768, Louis Dutens edited the first multi-volume collection of Leibniz’s writings. Later, in the 19th century, other editors, including Erdmann, Foucher de Careil, Gerhardt, Gerland, Klopp, and Mollat, published more of his works. In the early 20th century, Bertrand Russell and Louis Couturat studied Leibniz’s ideas, helping to restore his reputation among philosophers in English-speaking countries. Leibniz had already influenced German thinkers like Bernhard Riemann. For example, Leibniz’s phrase salva veritate, meaning "without losing the truth," appeared in the writings of Willard Quine. However, serious study of Leibniz’s work grew more common only after World War II. In the United States, scholars like Leroy Loemker helped promote Leibniz’s ideas through translations and essays. Philosophers such as Gilles Deleuze also praised Leibniz, writing about him in 1988.

Nicholas Jolley has suggested that Leibniz’s reputation as a philosopher is now stronger than it was during his lifetime. Modern philosophers still use his ideas about identity, how things become unique, and possible worlds. Research into the history of 17th- and 18th-century thought has shown how important the "Intellectual Revolution" of that time was, even though it is less well-known than the Industrial and commercial revolutions.

In Germany, many important institutions are named after Leibniz. In Hanover, he is honored with:
– Leibniz University Hannover
– Leibniz-Akademie, a training center for business professionals
– Gottfried Wilhelm Leibniz Bibliothek, one of Germany’s largest academic libraries
– Gottfried-Wilhelm-Leibniz-Gesellschaft, an organization that promotes Leibniz’s teachings
– Leibniz Association in Berlin
– Leibniz Scientific Society, a group of scientists in Berlin
– Leibniz Kolleg at Tübingen University, which helps high school graduates prepare for university
– Leibniz Supercomputing Centre in Munich
– Over 20 schools across Germany

Other honors include:
– Leibniz-Ring-Hannover, an award given to notable individuals in Hanover
– Leibniz-Medaille of the Berlin-Brandenburg Academy of Sciences and Humanities
– Gottfried-Wilhelm-Leibniz-Medaille of the Leibniz-Sozietät
– Leibniz-Medaille of the Mainz Academy of Sciences and Literature

In 1985, the German government created the Leibniz Prize, which gives up to €2.5 million annually to 10 scientists. It was the largest scientific award in the world before the Fundamental Physics Prize.

The collection of Leibniz’s handwritten papers at the Gottfried Wilhelm Leibniz Bibliothek was added to UNESCO’s Memory of the World Register in 2007.

Leibniz remains a popular figure today. A Google Doodle on July 1, 2018, celebrated his 372nd birthday, showing him writing "Google" in binary code with a quill. Voltaire’s Candide, published in 1759, was one of the first widely read but indirect introductions to Leibniz’s ideas. In the book, Leibniz is mocked as Professor Pangloss, called "the greatest philosopher of the Holy Roman Empire."

Leibniz also appears in Neal Stephenson’s book series The Baroque Cycle, which Stephenson said was inspired by his study of Leibniz. He is also a character in Adam Ehrlich Sachs’s novel The Organs of Sense.

A German biscuit called Choco Leibniz is named after him. It is made by Bahlsen, a company based in Hanover, where Leibniz lived for 40 years before his death.

Writings and publication

Gottfried Wilhelm Leibniz wrote in three main languages: Latin used by scholars, French, and German. During his lifetime, he published many pamphlets and scholarly articles, but only two books on philosophy: De Arte Combinatoria and Théodicée. He also wrote many pamphlets, often anonymously, for the House of Brunswick-Lüneburg. One important pamphlet was De jure suprematum, which discussed the nature of sovereignty. After Leibniz died, one major book was published: Nouveaux essais sur l'entendement humain (New Essays on Human Understanding). He had not allowed this book to be published after the death of John Locke.

In 1895, when a scholar named Bodemann completed a list of all of Leibniz’s writings and letters, people realized how large his collection of writings was. This collection, called his Nachlass (collection of writings and letters), included about 15,000 letters sent to more than 1,000 people and over 40,000 other items. Many of these letters were as long as essays. Much of his writing, especially letters from after 1700, has not yet been published. Most of what has been published appeared only in recent years. A list of more than 67,000 records from the Leibniz-Edition includes almost all of his known writings and letters.

The large number, variety, and disorganization of Leibniz’s writings are the result of a situation he described in a letter. The parts of the Leibniz-Edition that have been published are organized into eight series:

• Series 1: Political, Historical, and General Correspondence (25 volumes, 1666–1706).
• Series 2: Philosophical Correspondence (3 volumes, 1663–1700).
• Series 3: Mathematical, Scientific, and Technical Correspondence (8 volumes, 1672–1698).
• Series 4: Political Writings (9 volumes, 1667–1702).
• Series 5: Historical and Linguistic Writings (in preparation).
• Series 6: Philosophical Writings (7 volumes, 1663–1690, and Nouveaux essais sur l'entendement humain).
• Series 7: Mathematical Writings (6 volumes, 1672–1676).
• Series 8: Scientific, Medical, and Technical Writings (1 volume, 1668–1676).

The effort to organize all of Leibniz’s writings began in 1901. This work faced challenges during World War I and World War II, and later because of the division of Germany into East and West Germany. Scholars were separated, and parts of his writings were scattered. The project has dealt with writings in seven languages and over 200,000 pages. In 1985, the project was reorganized and became part of a joint effort by German federal and state academies. Since then, branches in Potsdam, Münster, Hanover, and Berlin have published 57 volumes of the Leibniz-Edition, each about 870 pages long, and created indexes and reference guides.

The year listed is usually when the work was completed, not when it was published.

• 1666 (published 1690): De Arte Combinatoria (On the Art of Combination); partially translated in Loemker (1969) and Parkinson (1966)
• 1667: Nova Methodus Discendae Docendaeque Iurisprudentiae (A New Method for Learning and Teaching Jurisprudence)
• 1667: Dialogus de connexione inter res et verba (A Dialogue About the Connection Between Things and Words)
• 1671: Hypothesis Physica Nova (New Physical Hypothesis)
• 1673: Confessio philosophi (A Philosopher’s Creed)
• October 1684: Meditationes de cognitione, veritate et ideis (Meditations on Knowledge, Truth, and Ideas)
• November 1684: Nova methodus pro maximis et minimis (New Method for Maximums and Minimums)
• 1686: Discours de métaphysique
• 1686: Generales inquisitiones de analysi notionum et veritatum (General Inquiries About the Analysis of Concepts and of Truths)
• 1694: De primae philosophiae Emendatione, et de Notione Substantiae (On the Correction of First Philosophy and the Notion of Substance)
• 1695: Système nouveau de la nature et de la communication des substances (New System of Nature)
• 1700: Accessiones historicae
• 1703: Explication de l'Arithmétique Binaire (Explanation of Binary Arithmetic)
• 1704 (published 1765): Nouveaux essais sur l'entendement humain
• 1707–1710: Scriptores rerum Brunsvicensium (3 volumes)
• 1710: Théodicée
• 1714: Principes de la nature et de la Grâce fondés en raison
• 1714: Monadologie

• 1717: Collectanea Etymologica, edited by Johann Georg von Eckhart, Leibniz’s secretary
• 1749: Protogaea
• 1750: Origines Guelficae

Six important collections of English translations include Wiener (1951), Parkinson (1966), Loemker (1969), Ariew & Garber (1989), Woolhouse & Francks (1998), and Strickland (2006).

The work of collecting, organizing, and publishing Leibniz’s writings, which began in 1901, is still ongoing as of 2025. This effort is led by the editorial project *